Help! I screwed up. Deep sink with disposer

Total oversight on my part- Kitchen cabinets are in and grante counters with sink are now installed. In installing the granite counter- they also installed a 9' deep "undermount" sink. When I went to eyeball the garbage disposal install I notice the outlet from the disposal is 2-3" lower than my drain. I cannot lower the drain at all since it comes in from the side wall and making it any lower would throw off the natural pitch out the main. I can buy another sink which is same dimensions but 7.5" deep but I don't think that helps me enough. Do they make any disposals where the outlet is less than 6" down???
I'm beside myself knowing I made this poor error and feel there is no way out.
HELP

thanks Jimbo- Can't lower the drain (even if before cabinets)- Drain comes in from other side of wall (which is basement)-
Kitchen is on a slab and that wall behind the sink is actually the basement ceiling. From there the drain goes to a 90 degree to the right and slopes down to the main out about 20' to the right. Someone mentioned some type of additional pump under there to move that water-- Or as long as you keep engaging disposal- won't it force the water out?

I've seen plenty of deep sinks now and the water does stay in the disposer.
It sucks!
Well, no it doesn't suck. That's the problem. Water needs to drain downhill.
The new standard for drains with deep sinks and disposers is 16" off the floor or lower.

Thanks Terry- I will try and talk the wife into eliminating the Disposal (or try to find a shallower sink)- if I lose the battle and hook this up- what are the remifications? just the water sitting stagnant?

Last dumb question (i will probably elimate the disposer) Someone at work mentioned using a small water pump like with a float somewhere in the circuit- Do they even make something for this purpose? Sounds like it might be more trouble that it's worth

The interior of the disposer is metal and it will ALWAYS be underwater. What happens to metal when it is continually immersed in water? Rust and deterioration. Plus, since the disposer is a pump, when it is turned on, the standing water will cause an imbalance until it is pumped out, creating serious vibration, especially with a stainless steel sink. Normal usage would prevent stagnation. In order to facilitate replacements, most disposers conform to a standard outlet dimension. At one time GE, the makers of "Disposals", made a small Disposal which sounded like a pencil sharpener when it operated, but now it also has the same dimension for the outlet.